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I've become really interested lately in the Wolfram Language and using it to work through problems in physics. I'm in a first year course in classical mechanics right now, and I was wondering if anyone had any insight into how these types of problems (easy kinematics and dynamics) could be modelled in Mathematica.

I've found a couple books on the subject but they're way above my level, using some mathematics I haven't fully learned yet. Does anyone have any ideas or resources into how you could solve basic dynamics problems using the Wolfram Language?

Right now, the best idea I have is to write some custom functions/modules that will compute position/velocity/acceleration at a given time given certain equations of motion. But I'm not sure how to define a function like that, one that depends on many variables that may or may not be unknown. Could I write a module that will just operate on the kinematic equations for a certain situation (projectile without drag, uniform circular motion) and animate the motion? Anyone have any links or tutorials?

Alternatively, does anyone happen to know if a certain part of the mathematica documentation covers those kinds of modules/functions? I've been looking through but I'm very new to programming (in any language) and I'm finding it a little overwhelming.

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    $\begingroup$ I think this would do better on Mathematica, particularly if it's rewritten to focus on a single concrete example. $\endgroup$
    – WillO
    Commented Jun 6, 2020 at 17:40
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    $\begingroup$ The NDSolve function can numerically integrate differential equations of motion. See Examples > Applications > Mechanical Systems for some examples. $\endgroup$
    – G. Smith
    Commented Jun 6, 2020 at 17:43
  • $\begingroup$ You might consider the book "A Physicist's Guide to Mathematica" by Tam and there are a few other books of similar ilk. $\endgroup$
    – K7PEH
    Commented Jun 6, 2020 at 21:19

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I recommend

De Lange, O.L. and Pierrus, J., 2010. Solved problems in classical mechanics: Analytical and numerical solutions with comments. Oxford University Press

It contains a mixture of theory and numerical exercices, and all the numerical stuff is done using Mathematica. The book contains multiple levels of exercices and detailed complete Mathematica notebooks, especially in the late chapters where the problems become non-trivial.

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I am not familiar with Mathematica, but I can give you an approach for solving basic mechanics problems: 1. Sketch the situation. 2. Put in vectors to represent each force. 3. Define your symbols on the sketch. 4. For each mass in the system, write a component force equation (ΣF = ma) for each dimension of motion. 5. If relevant, write a torque equation (Usually one will do for torques about the center of mass. You may want to consider an instantaneous axis of rotation. In a static situation any choice of axis will do. ) 6. Make sure all measurements are in the same system of units. 7. Put known values into your equations. 8. Let Mathematica solve for the unknowns. (I have a spreadsheet that does this and another one for basic kinematics.)

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